1. Field of the Invention
The present invention relates to a band-pass filter (BPF), and more particularly, to controlling a BPF's center frequency.
2. Discussion of the Related Art
FIG. 1 shows a configuration of a conventional BPF. As shown in FIG. 1, a conventional BPF is constructed in such a manner that one end of a capacitor C1 is coupled to the input port in of an AC voltage source Vi, the other end of capacitor C1 is coupled to the noninverting input port + of a transconductance amplifier 2, the inverting input port - of transconductance amplifier 2 is coupled to the output port of transconductance amplifier 2 via a resistor R2, a resistor R1 is coupled to the inverting input port - of transconductance amplifier 2 and the ground, the inverting input port - of transconductance amplifier 1 is coupled to the output port of transconductance amplifier 2, the noninverting input port + of transconductance amplifier 1 is coupled to ground, the noninverting input port + of transconductance amplifier 2 is coupled to the output port of transconductance amplifier 1, and a variable resistor Rext is coupled between a power source Vcc and filter controlling port 4. In short, the center frequency f0 of conventional BPF is controlled by feeding back transconductance amplifiers 1 and 2 and controlling variable resistor Rext.
FIG. 2 is an equivalent circuit diagram of transconductance amplifier 2 of FIG. 1. In FIG. 2, the equivalent circuit of transconductance amplifier 2 consists of a pnp transistor Q5 whose emitter is coupled to power Vcc and whose collector and base are coupled to the ground, a pnp transistor Q4 whose emitter is coupled to power Vcc and whose base is coupled to the base and collector of pnp transistor Q5, a capacitor C2 coupled to the collector of pnp transistor Q5 and the ground, an npn transistor Q7 whose collector is coupled to power Vcc and whose base is coupled to a bias input BIAS, an npn transistor Q8 whose collector is coupled to power Vcc and whose base is coupled to bias input BIAS, an npn transistor Q2 whose base is coupled to the emitter of npn transistor Q7 and whose collector is coupled to power Vcc, an npn transistor Q3 whose collector is coupled to the collector of pnp transistor Q4 and whose base is coupled to the emitter of npn transistor Q8, an npn transistor Q6 whose collector is coupled to the emitter of npn transistor Q8 and whose base is coupled to the ground, a resistor R5 coupled to the emitter of npn transistor Q6 and the ground, a variable resistor Rext coupled to power Vcc and filter controlling port 4, an npn transistor Q10 whose collector and base are coupled to filter controlling port 4 via resistor R6 and whose emitter is coupled to the ground via resistor R7, an npn transistor Q9 whose collector is coupled to the emitter of npn transistors Q2 and Q3, whose base is coupled to filter controlling port 4 and whose emitter is coupled to the ground via resistor R4, and an npn transistor Q1 whose base is coupled to input voltage Vi' whose collector is coupled to the emitter of transistor Q7 and whose emitter is coupled to the ground via resistor R3.
Here, pnp transistors Q4 and Q5 form a current mirror 6, while npn transistors Q1, Q2, Q3, Q6, and Q7 and resistors R3, R4, and R5 form a differential amplifier 5. An input/output transfer function Av(S) and center frequency f0 of the conventional BPF of FIGS. 1 and 2 are given in the following equations.
First, the Laplace-transformed input/output transfer function of the BPF is: ##EQU1## where GM indicates the ratio of input voltage and output current. ##EQU2##
Center frequency f0 is determined by the ratio (GM) of input/output current of transconductance amplifier 2. As shown in FIG. 2, input/output current ratio GM is obtained by: ##EQU3## Center frequency f0 is given by the following equation according to equations 2 and 4: ##EQU4##
When variable resistor Rext between power Vcc and filter controlling port 4 is controlled, currents flowing through npn transistor Q8 are converted, and current I.sub.1 is changed by the current mirror of npn transistors Q4 and Q5. Thus, center frequency f0 is controlled in accordance with equation 5. In other words, when variable resistor Rext is controlled, center frequency f0 of the conventional BPF is controlled. However, in the conventional BPF, resistors, condensers, and constant current devices have deviations so that center frequency f0 must be controlled initially, increasing the number of processes, production cost, and processing time on the production line.